Calculus 1

Cards (10)

• 1
  Front

  What does the Fundamental Theorem of Calculus (Part 1) state?

  Back

  If F is an antiderivative of f on [a, b], then the integral from a to b of f(x)dx equals F(b) - F(a).

• 2
  Front

  What is the formal definition of a derivative?

  Back

  f'(x) = lim(h→0) [f(x+h) - f(x)] / h, provided the limit exists.

• 3
  Front

  What does it mean for a function to be continuous at a point x = c?

  Back

  f is continuous at x = c if: f(c) is defined, lim(x→c) f(x) exists, and lim(x→c) f(x) = f(c).

• 4
  Front

  State the Power Rule for differentiation.

  Back

  If f(x) = x^n, then f'(x) = n·x^(n-1), where n is any real number.

• 5
  Front

  State the Chain Rule for differentiation.

  Back

  If h(x) = f(g(x)), then h'(x) = f'(g(x)) · g'(x).

• 6
  Front

  What is the Product Rule for differentiation?

  Back

  If h(x) = f(x)·g(x), then h'(x) = f'(x)·g(x) + f(x)·g'(x).

• 7
  Front

  What is the Quotient Rule for differentiation?

  Back

  If h(x) = f(x)/g(x), then h'(x) = [f'(x)·g(x) - f(x)·g'(x)] / [g(x)]^2.

• 8
  Front

  How are critical points used in finding the absolute extrema of a function on a closed interval?

  Back

  Evaluate the function at all critical points (where f'(x) = 0 or f'(x) is undefined) within the interval and at the endpoints; the largest value is the absolute maximum and the smallest is the absolute minimum.

• 9
  Front

  What is the basic Power Rule for integration?

  Back

  The integral of x^n dx equals x^(n+1)/(n+1) + C, for n ≠ -1.

• 10
  Front

  What does the second derivative of a function tell you about its graph?

  Back

  The second derivative indicates concavity: f''(x) > 0 means the graph is concave up, and f''(x) < 0 means the graph is concave down. Points where concavity changes are inflection points.